[libcxx] Improve accuracy of complex asinh and acosh
Summary:
Currently std::asinh and std::acosh use std::pow to compute x^2. This
results in a significant error when computing e.g. asinh(i) or
acosh(-1).
This patch expresses x^2 directly via x.real() and x.imag(), like it
is done in libstdc++/glibc, and adds tests that checks the accuracy.
Reviewers: EricWF, mclow.lists
Reviewed By: mclow.lists
Subscribers: christof, cfe-commits
Differential Revision: https://reviews.llvm.org/D41629
git-svn-id: https://llvm.org/svn/llvm-project/libcxx/trunk@325510 91177308-0d34-0410-b5e6-96231b3b80d8
diff --git a/include/complex b/include/complex
index c7c1cde..d692ee3 100644
--- a/include/complex
+++ b/include/complex
@@ -1125,6 +1125,17 @@
return _VSTD::pow(result_type(__x), result_type(__y));
}
+// __sqr, computes pow(x, 2)
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+__sqr(const complex<_Tp>& __x)
+{
+ return complex<_Tp>((__x.real() - __x.imag()) * (__x.real() + __x.imag()),
+ _Tp(2) * __x.real() * __x.imag());
+}
+
// asinh
template<class _Tp>
@@ -1150,7 +1161,7 @@
}
if (__libcpp_isinf_or_builtin(__x.imag()))
return complex<_Tp>(copysign(__x.imag(), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
- complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) + _Tp(1)));
+ complex<_Tp> __z = log(__x + sqrt(__sqr(__x) + _Tp(1)));
return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
}
@@ -1184,7 +1195,7 @@
}
if (__libcpp_isinf_or_builtin(__x.imag()))
return complex<_Tp>(abs(__x.imag()), copysign(__pi/_Tp(2), __x.imag()));
- complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
+ complex<_Tp> __z = log(__x + sqrt(__sqr(__x) - _Tp(1)));
return complex<_Tp>(copysign(__z.real(), _Tp(0)), copysign(__z.imag(), __x.imag()));
}
@@ -1318,7 +1329,7 @@
return complex<_Tp>(__pi/_Tp(2), -__x.imag());
if (__x.real() == 0 && (__x.imag() == 0 || isnan(__x.imag())))
return complex<_Tp>(__pi/_Tp(2), -__x.imag());
- complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
+ complex<_Tp> __z = log(__x + sqrt(__sqr(__x) - _Tp(1)));
if (signbit(__x.imag()))
return complex<_Tp>(abs(__z.imag()), abs(__z.real()));
return complex<_Tp>(abs(__z.imag()), -abs(__z.real()));
diff --git a/test/libcxx/numerics/complex.number/__sqr.pass.cpp b/test/libcxx/numerics/complex.number/__sqr.pass.cpp
new file mode 100644
index 0000000..a3cc9dd
--- /dev/null
+++ b/test/libcxx/numerics/complex.number/__sqr.pass.cpp
@@ -0,0 +1,81 @@
+//===----------------------------------------------------------------------===//
+//
+// The LLVM Compiler Infrastructure
+//
+// This file is dual licensed under the MIT and the University of Illinois Open
+// Source Licenses. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+
+// <complex>
+
+// template<class T>
+// complex<T>
+// __sqr(const complex<T>& x);
+
+#include <complex>
+#include <cassert>
+
+template <class T>
+void
+test()
+{
+ const T tolerance = std::is_same<T, float>::value ? 1.e-6 : 1.e-14;
+
+ typedef std::complex<T> cplx;
+ struct test_case
+ {
+ cplx value;
+ cplx expected;
+ };
+
+ const test_case cases[] = {
+ {cplx( 0, 0), cplx( 0, 0)},
+ {cplx( 1, 0), cplx( 1, 0)},
+ {cplx( 2, 0), cplx( 4, 0)},
+ {cplx(-1, 0), cplx( 1, 0)},
+ {cplx( 0, 1), cplx(-1, 0)},
+ {cplx( 0, 2), cplx(-4, 0)},
+ {cplx( 0, -1), cplx(-1, 0)},
+ {cplx( 1, 1), cplx( 0, 2)},
+ {cplx( 1, -1), cplx( 0, -2)},
+ {cplx(-1, -1), cplx( 0, 2)},
+ {cplx(0.5, 0), cplx(0.25, 0)},
+ };
+
+ const unsigned num_cases = sizeof(cases) / sizeof(test_case);
+ for (unsigned i = 0; i < num_cases; ++i)
+ {
+ const test_case& test = cases[i];
+ const std::complex<T> actual = std::__sqr(test.value);
+ assert(std::abs(actual.real() - test.expected.real()) < tolerance);
+ assert(std::abs(actual.imag() - test.expected.imag()) < tolerance);
+ }
+
+ const cplx nan1 = std::__sqr(cplx(NAN, 0));
+ assert(std::isnan(nan1.real()));
+ assert(std::isnan(nan1.imag()));
+
+ const cplx nan2 = std::__sqr(cplx(0, NAN));
+ assert(std::isnan(nan2.real()));
+ assert(std::isnan(nan2.imag()));
+
+ const cplx nan3 = std::__sqr(cplx(NAN, NAN));
+ assert(std::isnan(nan3.real()));
+ assert(std::isnan(nan3.imag()));
+
+ const cplx inf1 = std::__sqr(cplx(INFINITY, 0));
+ assert(std::isinf(inf1.real()));
+ assert(inf1.real() > 0);
+
+ const cplx inf2 = std::__sqr(cplx(0, INFINITY));
+ assert(std::isinf(inf2.real()));
+ assert(inf2.real() < 0);
+}
+
+int main()
+{
+ test<float>();
+ test<double>();
+ test<long double>();
+}
diff --git a/test/std/numerics/complex.number/complex.transcendentals/acosh.pass.cpp b/test/std/numerics/complex.number/complex.transcendentals/acosh.pass.cpp
index deb056d..5258bdc 100644
--- a/test/std/numerics/complex.number/complex.transcendentals/acosh.pass.cpp
+++ b/test/std/numerics/complex.number/complex.transcendentals/acosh.pass.cpp
@@ -54,6 +54,15 @@
assert(r.imag() == 0);
assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
}
+ else if (testcases[i].real() == -1 && testcases[i].imag() == 0)
+ {
+ assert(r.real() == 0);
+ assert(!std::signbit(r.real()));
+ if (std::signbit(testcases[i].imag()))
+ is_about(r.imag(), -pi);
+ else
+ is_about(r.imag(), pi);
+ }
else if (std::isfinite(testcases[i].real()) && std::isinf(testcases[i].imag()))
{
assert(std::isinf(r.real()));
diff --git a/test/std/numerics/complex.number/complex.transcendentals/asinh.pass.cpp b/test/std/numerics/complex.number/complex.transcendentals/asinh.pass.cpp
index 3da56c3..cb9188d 100644
--- a/test/std/numerics/complex.number/complex.transcendentals/asinh.pass.cpp
+++ b/test/std/numerics/complex.number/complex.transcendentals/asinh.pass.cpp
@@ -44,6 +44,15 @@
assert(std::signbit(r.real()) == std::signbit(testcases[i].real()));
assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
}
+ else if (testcases[i].real() == 0 && std::abs(testcases[i].imag()) == 1)
+ {
+ assert(r.real() == 0);
+ assert(std::signbit(testcases[i].imag()) == std::signbit(r.imag()));
+ if (std::signbit(testcases[i].imag()))
+ is_about(r.imag(), -pi/2);
+ else
+ is_about(r.imag(), pi/2);
+ }
else if (std::isfinite(testcases[i].real()) && std::isinf(testcases[i].imag()))
{
assert(std::isinf(r.real()));